We are given the results of a survey about the sale of books in each quarter. Let's design a simulation to estimate the probability that a random book will be sold in each quarter. First let's review the steps for designing a simulation.
Choose and describe an appropriate probability model for the situation.
Define a trial for the situation and choose the number of trials to be conducted.
Let's follow these steps, one at a time.
Step 1
Since we are interested in the probability that a random book will be sold in each of the 4 quarters of a year, we have 4 possible outcomes. Based on the given information, we will assume that the theoretical probability that a book will be sold in a particular quarter is equal to the given percentages.
Possible Outcomes
Theoretical Probability
January, February, March
22 %
April, May, June
23 %
July, August, September
25 %
October, November, December
30 %
Step 2
We will also assume that the trends in selling the books stay approximately constant during the time period.
Step 3
Since we are asked to use a geometric probability model, we can use a spinner divided into 4 sectors — each sector representing one of the probabilities. Let's calculate the measure of the central angle of each sector.
Possible Outcomes
Measure of the Central Angle
January, February, March
22 %* 360^(∘)=79.2^(∘)
April, May, June
23 %*360^(∘)=82.8^(∘)
July, August, September
25 %*360^(∘)=90^(∘)
October, November, December
30 %*360^(∘)=108^(∘)
Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the quarter in which a random book is sold.
Step 4
Finally, let's choose the number of trials to be 50. The results of conducting the described simulation can be recorded in a frequency table and used to evaluate the experimental probabilities. Keep in mind that this is just one possible simulation we can create.
